Measures of noncompactness and essential pseudospectra on Banach space

Abstract

In this research article, we work with the notion of the measures of noncompactness in order to establish some results concerning the essential pseudospectra of closed, densely defined linear operators in the Banach space. We start by giving a refinement of the definition of the essential pseudospectra by means of the measure of noncompactness, and we give sufficient conditions on the perturbed operator to have its invariance.

Essential pseudospectra and essential norms of band-dominated operators

“…Particularly related is the work of Trefethen, Embree and others (see [41] and references therein) on pseudospectra. We probably have to mention [1,2], where essential pseudospectra have been defined.…”

“…Under these operations, the map A → ϕ A | ∂Z N = (1.2) turns out to be an algebra homomorphism. Now the crucial point is that K(X, P) is exactly the kernel of that homomorphism A → (1.2), whence (1.1) → (1.2) is a well-defined algebra isomorphism 2 . In short: The set (1.2) nicely reflects the coset (1.1).…”

A note on the essential pseudospectra and application

“…In Ammar and Jeribi [5][6][7] defined the notion of Weyl pseudospectra of densely closed defined, linear operators in the Banach space by:…”

“…[6][7][8][9] Throughout this paper, let X , Y ... denote infinite dimensional Banach spaces over K = R or C and we denote by L(X, Y ) (resp. C(X, Y )) the set of all bounded (resp.…”

Pseudospectra in a non-Archimedean Banach space and essential pseudospectra in Eω

“…where K (X) designates the subspace of all compact operator on X. Inspired by the notions of pseudospectra and essential spectrum, the new concept of the essential pseudospectra was declared (see [1][2][3][4]). In [2], A. Ammar and A. Jeribi introduced the notion of Weyl pseudospectra of densely closed, linear operator A in a Banach space X which is defined by…”